Pseudo Random Binary Sequence Generated by Trace and Legendre Symbol with Non Primitive Element in $\mathbb{F}_{p^2}$

Chiaki Ogawa; Ali M. Arshad; Yasuyuki Nogami; Satoshi Uehara; Kazuyoshi Tsuchiya; Robert Morelos Zaragoza

Summary

International Symposium on Nonlinear Theory and Its Applications

2016

Session Number:A4L-C

Session:

Number:A4L-C-4

Pseudo Random Binary Sequence Generated by Trace and Legendre Symbol with Non Primitive Element in $\mathbb{F}_{p^2}$

Chiaki Ogawa, Ali M. Arshad, Yasuyuki Nogami, Satoshi Uehara, Kazuyoshi Tsuchiya, Robert Morelos Zaragoza,

pp.-

Publication Date:2016/11/27

Online ISSN:2188-5079

DOI:10.34385/proc.48.A4L-C-4

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Summary:

Pseudo binary random sequence has many uses such as nonce for security applications. Some of them needs to have long period and high linear complexity. The authors have proposed a generation method that uses primitive polynomial, trace function, and Legendre symbol over odd characteristic field. The preparation of primitive polynomial is not always easy. This paper shows that some non-primitive irreducible polynomials generate the same random binary sequence generated by a certain primitive polynomial. Then, some example are also introduced.